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Basic Ideas to Approach Metastability in Probabilistic Cellular Automata

  • Emilio N. M. Cirillo
  • Francesca R. Nardi
  • Cristian SpitoniEmail author
Chapter
Part of the Emergence, Complexity and Computation book series (ECC, volume 27)

Abstract

Cellular Automata are discrete-time dynamical systems on a spatially extended discrete space, which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete-time Markov chains on lattice with finite single-cell states whose distinguishing feature is the parallel character of the updating rule. We review the some of the results obtained about the metastable behavior of Probabilistic Cellular Automata, and we try to point out difficulties and peculiarities with respect to standard Statistical Mechanics Lattice models.

Keywords

Reversible PCA Metastability Potential theoretic approach 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Emilio N. M. Cirillo
    • 1
  • Francesca R. Nardi
    • 2
    • 3
    • 4
  • Cristian Spitoni
    • 5
    Email author
  1. 1.Dipartimento di Scienze di Base e Applicate per l’IngegneriaUniversità di Roma: la SapienzaRomaItaly
  2. 2.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.EurandomEindhovenThe Netherlands
  4. 4.Dipartmento di Matematica e InformaticaUniversitá di FirenzeFirenzeItaly
  5. 5.Institute of MathematicsUniversity of UtrechtUtrechtThe Netherlands

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